Performance of primal-dual algorithms for multi-channel image reconstruction in spectral X-ray CT

The development of spectral X-ray CT using binned photon-counting detectors has enabled an imaging technique called K-edge imaging. This concept allows the selective and quantitative imaging of contrast agents loaded with K-edge materials. However, current limitations in detector hardware result in high-noise levels present in material-decomposed sinograms. Recently, the spectral X-ray CT reconstruction problem was formulated within a multi-channel (MC) framework using a penalized weighted least squares (PWLS) estimator in which statistical correlations between the decomposed material sinograms can be exploited to improve image quality. Such an approach allows the use of any number of basis materials and is therefore applicable to photon-counting systems and K-edge imaging. The preliminary study results demonstrated the advantages of exploiting inter-sinogram correlations which are neglected in conventional (statistically-principled) reconstruction methods where the material-decomposed sinograms are treated individually. However, the utilization of inter-sinogram correlations, in particular in combination with modern sparsity-promoting penalties, results in numerical challenges in developing efficient reconstruction algorithms. In this work, the numerical performance of state-of-the-art primal-dual algorithms to minimize the MC PWLS objective function is investigated. The numerical schemes include the alternating direction method of multipliers (ADMM) and an ADMM related strategy, as well as the Chambolle-Pock´s primal-dual algorithm. A computer-simulation phantom is conducted to simulate spectral X-ray CT measurements and used to evaluate the performance of algorithms.